Let's evaluate each statement:
Statement I: SnF\(_4\) is ionic in nature.
Tin (Sn) is a Group 14 element. Fluorine (F) is highly electronegative.
Generally, tetrahalides of Group 14 elements (like CCl\(_4\), SiCl\(_4\), GeCl\(_4\)) are covalent. However, as we move down the group, the metallic character increases, and the tendency to form ionic compounds also increases.
Furthermore, with highly electronegative elements like fluorine, the electronegativity difference with tin is significant. While not perfectly ionic, SnF\(_4\) exhibits substantial ionic character, unlike the more covalent nature of halides of lighter Group 14 elements (e.g., CCl\(_4\), SiF\(_4\)). Therefore, this statement is generally considered correct.
Statement II: Stability of dihalides of group 14 elements increases down the group.
Group 14 elements can exhibit +2 and +4 oxidation states. As we move down the group from C to Pb, the stability of the +2 oxidation state increases due to the inert pair effect. This effect describes the increasing reluctance of the \(ns^2\) valence electrons to participate in bonding.
For example, CCl\(_2\) and SiCl\(_2\) are very unstable. GeCl\(_2\) is somewhat stable but reactive. SnCl\(_2\) is stable. PbCl\(_2\) is very stable and is the more common halide of lead.
Thus, the stability of dihalides (compounds in the +2 oxidation state) indeed increases down Group 14. This statement is correct.
Statement III: GeCl\(_2\) is more stable than GeCl\(_4\).
For Germanium (Ge), which is positioned above Tin and Lead in Group 14, the inert pair effect is not as pronounced as it is for Sn and Pb. While Ge can form compounds in the +2 oxidation state, the +4 oxidation state is still generally more stable. GeCl\(_4\) is a stable compound, whereas GeCl\(_2\) is less stable and acts as a strong reducing agent (meaning it readily gets oxidized to Ge(+4)). The statement would be correct for Lead (e.g., PbCl\(_2\) is more stable than PbCl\(_4\)), but not for Germanium. Therefore, this statement is incorrect.
Conclusion:
Statements I and II are correct. Statement III is incorrect.
The option that contains only correct statements (I and II) is the answer.
The final answer is \( \boxed{\text{I \& II only}} \).